(*** after_uni_dx *)
lemma gr_after_nat_uni (l2) (l1):
∀f2. @↑❪l1, f2❫ ≘ l2 →
- â\88\80f. f2 â\8a\9a ð\9d\90®â\9d¨l1â\9d© â\89\98 f â\86\92 ð\9d\90®â\9d¨l2â\9d© â\8a\9a ⫱*[l2] f2 ≘ f.
+ â\88\80f. f2 â\8a\9a ð\9d\90®â\9d¨l1â\9d© â\89\98 f â\86\92 ð\9d\90®â\9d¨l2â\9d© â\8a\9a â«°*[l2] f2 ≘ f.
#l2 @(nat_ind_succ … l2) -l2
[ #l1 #f2 #Hf2 #f #Hf
elim (gr_nat_inv_zero_dx … Hf2) -Hf2 // #g2 #H1 #H2 destruct
(*** after_uni_sn *)
lemma gr_nat_after_uni_tls (l2) (l1):
∀f2. @↑❪l1, f2❫ ≘ l2 →
- â\88\80f. ð\9d\90®â\9d¨l2â\9d© â\8a\9a ⫱*[l2] f2 ≘ f → f2 ⊚ 𝐮❨l1❩ ≘ f.
+ â\88\80f. ð\9d\90®â\9d¨l2â\9d© â\8a\9a â«°*[l2] f2 ≘ f → f2 ⊚ 𝐮❨l1❩ ≘ f.
#l2 @(nat_ind_succ … l2) -l2
[ #l1 #f2 #Hf2 #f #Hf
elim (gr_nat_inv_zero_dx … Hf2) -Hf2 // #g2 #H1 #H2 destruct